Angle between lines

Calculate the angle between these two lines:

p:−4x+7y+7=0
q:−x+4y+7=0

Correct answer:

θ =  20.6 °

Step-by-step explanation:

n=(−4,7) m=(−1,4)  x1​=ny​nx​​=7(−4)​=−74​≐−0.5714 x2​=my​mx​​=4(−1)​=−41​=−0.25  θ1​=arctan(1−x1​⋅ x2​∣x1​−x2​∣​)=arctan(1−(−0.5714)⋅ (−0.25)∣(−0.5714)−(−0.25)∣​)≐0.3588 rad  θ=θ1​→  °=θ1​⋅ π180​   °=0.3588⋅ π180​   °=20.6  °=20.6∘=20°33′22"

Try another example


Did you find an error or inaccuracy? Feel free to write us. Thank you!







Tips for related online calculators
The line slope calculator is helpful for basic calculations in analytic geometry. The coordinates of two points in the plane calculate slope, normal and parametric line equation(s), slope, directional angle, direction vector, the length of the segment, intersections of the coordinate axes, etc.
See also our trigonometric triangle calculator.
Try conversion angle units angle degrees, minutes, seconds, radians, grads.

You need to know the following knowledge to solve this word math problem:

Units of physical quantities:

Grade of the word problem:


 
We encourage you to watch this tutorial video on this math problem: video1   video2

Related math problems and questions: